| We consider completely integrable Hamiltonian equations
like Euler-Poisson equations of a rigid body around a fixed point and Kirchoff
equations describing the motion of a particle in an ideal fluid. These
equations possess a Hamiltonian,
two Casimirs and for the integrable cases an additional fourth integral. They are integrated numerically by using the reflexive updating formula
which preserves the time-reversibility of the flow and a Hamiltonian splitting
method which preserves the underlying
Numerical solutions reveals that the Hamiltonian, Casimirs and the additional integral errors remain bounded for long-time integration for both methods. The Casimirs are exactly preserved for the Hamiltonian splitting. The periodicity of the numerical solutions are retained the Hamiltonian splitting method. Keywords: Hamiltonian systems, complete integrability, Poisson
structure, reversible integrators, splitting methods
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